A258730 T(n,k)=Number of length n+k 0..3 arrays with at most one downstep in every k consecutive neighbor pairs.

16, 60, 64, 190, 225, 256, 512, 608, 840, 1024, 1212, 1408, 2028, 3136, 4096, 2592, 2936, 4184, 6552, 11704, 16384, 5115, 5664, 7834, 12549, 20955, 43681, 65536, 9460, 10280, 13720, 21860, 35540, 68120, 163020, 262144, 16588, 17754, 22866, 35704

Offset: 1

Author

R. H. Hardin, Jun 08 2015

Keywords

• nonn
• tabl

Comments

Table starts

......16......60.....190.....512....1212....2592....5115....9460....16588

......64.....225.....608....1408....2936....5664...10280...17754....29416

.....256.....840....2028....4184....7834...13720...22866...36656....56925

....1024....3136....6552...12549...21860...35704...55660...83758...122584

....4096...11704...20955...35540...59188...92548..138196..199264...279560

...16384...43681...68120...98676..149960..228081..331584..465580...635992

...65536..163020..220854..281136..370510..526672..752180.1038256..1394568

..262144..608400..711432..819453..941024.1183616.1607656.2192682..2911776

.1048576.2270580.2300008.2358888.2487276.2727288.3343894.4392072..5783522

.4194304.8473921.7446144.6678576.6650600.6597449.7100132.8569478.10965340

Examples

			Some solutions for n=4 k=4
..1....1....0....0....3....0....1....3....2....0....2....3....0....3....2....0
..0....2....3....3....1....1....2....3....2....1....2....2....3....3....0....2
..2....0....3....1....1....1....3....3....0....1....3....3....0....0....2....2
..3....2....3....1....2....1....1....0....0....1....0....3....1....2....3....3
..3....3....3....1....2....1....1....0....1....1....0....3....3....3....3....0
..0....3....3....2....3....3....1....1....1....0....3....0....3....3....2....0
..0....3....1....3....0....0....2....3....2....0....3....2....1....0....2....2
..3....2....2....1....2....1....0....1....0....0....2....2....1....0....2....2
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..9999

Crossrefs

Column 1 is A000302(n+1)

Column 2 is A072335(n+2)

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1)

k=2: a(n) = 4*a(n-1) -4*a(n-3) +a(n-4)

k=3: [order 8]

k=4: [order 12]

k=5: [order 16]

k=6: [order 19]

k=7: [order 22]

Empirical for row n:

n=1: [polynomial of degree 7]

n=2: [polynomial of degree 7]

n=3: [polynomial of degree 7] for n>1

n=4: [polynomial of degree 7] for n>2

n=5: [polynomial of degree 7] for n>3

n=6: [polynomial of degree 7] for n>4

n=7: [polynomial of degree 7] for n>5